Home » fields

Category Archives: fields

Warp drive

Most people are familiar with warp drive as a form of FTL (Faster Than Light travel) Its most popular use is in the science-fiction series Star Trek. What is warp drive – and according to the laws of physics, as we know them today, could this potentially be possible?

Enterprise at warp speed Star Trek

Warp drive in science fiction


Warping space in general relativity



Gravity General Relativity warping The Elegant Universe

From “The Elegant Universe”, PBS series NOVA. 2003.

Warp drive in real physics

The Alcubierre drive is a speculative analysis of physics which shows that warp drive may in fact be possible. It is based on a solution of Einstein’s field equations in general relativity.  It was first proposed by Mexican theoretical physicist Miguel Alcubierre. In his analysis, a spacecraft could effectively achieve a kind of FTL travel if a configurable energy-density field lower than that of vacuum (that is, negative mass) could be created.

Alcubierre Warp Drive

From a demo on Wolfram.com by Thomas Mueller.

Rather than exceeding the speed of light within a local reference frame, a spacecraft would traverse distances by contracting space in front of it and expanding space behind it, resulting in effective faster-than-light travel.

In this analysis, objects still cannot accelerate to the speed of light within normal spacetime; therefore it doesn’t violate the laws of General Relativity.

Instead, the Alcubierre drive shifts space around an object so that the object would arrive at its destination faster than light would in normal space.

“Space-time bubble is the closest that modern physics comes to the “warp drive” of science fiction. It can convey a starship at arbitrarily high speeds. Space-time contracts at the front of the bubble, reducing the distance to the destination, and expands at its rear, increasing the distance from the origin (arrows). The ship itself stands still relative to the space immediately around it; crew members do not experience any acceleration. Negative energy (blue) is required on the sides of the bubble.” – Ford and Roman


Lawrence H. Ford and Thomas A. Roman. Sci Am article.



Although the metric proposed by Alcubierre is consistent with the Einstein field equations, it may not be physically meaningful. We are not certain that the mathematical solutions are possible in the real world. If so then this warp drive will not be possible.

Even if it is physically meaningful, that does not necessarily mean that a drive can be constructed. The proposed mechanism of the Alcubierre drive implies a negative energy density and therefore requires exotic matter. So if exotic matter with the correct properties can not exist, then the drive could not be constructed.

Further reading

Negative Energy. Wormholes and Warp Drive. Scientific American Jan 2000

Faster-than-light (FTL) Travel in Science Fiction. Dan Koboldt

Alcubierre warp drive, Wikipedia

Faster Than Light, Wikipedia

Negative Energy, Wormholes and Warp Drive, Scientific American, Jan 2000

By Lawrence H. Ford and Thomas A. Roman

Learning Standards

2016 Massachusetts Science and Technology Curriculum Framework
Appendix VIII: Value of Crosscutting Concepts and Nature of Science in Curricula

ETS3. Technological Systems.  5.3-5-ETS3-1(MA). Use informational text to provide examples of improvements to existing technologies (innovations) and the development of new technologies (inventions). Recognize that technology is any modification of the natural or designed world done to fulfill human needs or wants.

9. Influence of Engineering, Technology, and Science on Society and the Natural World

In grades 9–12, students can describe how modern civilization depends on major technological systems, such as agriculture, health, water, energy, transportation, manufacturing, construction, and communications. Engineers continuously modify these systems to increase benefits while decreasing costs and risks. New technologies can have deep impacts on society and the environment, including some that were not anticipated.

SAT Subject Test: Physics

Quantum phenomena, such as photons and photoelectric effect

Atomic, such as the Rutherford and Bohr models, atomic energy levels, and atomic spectra. Nuclear and particle physics, such as radioactivity, nuclear reactions, and fundamental particles. Relativity, such as time dilation, length contraction, and mass-energy equivalence.

College Board Standards for College Success: Science

Enduring Understanding 1D: Classica mechanics can not describe all properties of objects.


What are fields?

What are gravitational fields? Electric fields? Magnetic fields? the electromagnetic field?

What do physicists mean by the term “field”?

Imagine our universe is flat. We could describe what’s going on at any point by defining a 2D grid, like graph paper.

2-d field representing temperature

2-d field representing wind speed


Our universe is 3D. We need 3 dimensions – 3 axes – to describe any point in space.

This image shows an empty universe, with nothing in it.

Imagine this 3D grid extending through our world:

(indoor 3D climbing array by Croatian-Austrian artists  Sven Jonke, Christoph Katzler and Nikola Radeljković.)

Is our world filled with actual fields? Yes.

Our universe is filled with an electromagnetic field which allows magnetism to exist.

Consider a horseshoe magnet – it’s a 3D object, with a 3D magnetic field invisibly emanating from it. How can we visualize this invisible field? How about tossing in a few thousand small iron filings! 🙂

What’s special about the electromagnetic field? It isn’t really being created by the magnet – it is already everywhere. In us, around us, throughout the entire universe.

At every single point in our universe appears to be a vector electric field (has both magnitude and intensity), and a vector magnetic field. In fact, it turns out that there is really just one field – the electromagnetic field – that exists throughout our universe. And as particles move and interact with each other, the quantities at each point in this field change.

(image of magnetic field by cordelia molloy )

So imagine that each point in space – even the one right at your index finger’s tip, already has a value for an electromagnetic field. Maybe the value, at this moment, for both E and B is small, maybe even zero – but it still has a value.

As a magnet moves close to you, the values at each point in this field change. We can’t see it with our eyes or feel it with our fingers – but we can measure it by seeing the effect it has on a compass – or the effect it has on the magnetometer built into your cell phone (and yes, there’s an App for that!)

Physics Toolbox Magnetometer: google play


“Nickolay Lamm has already made the invisible visible with a project that showed what Wi-Fi would look like if we could see it, but for his latest series of images, the artist has turned his attention to cell phones. Cell phone networks across the country are made up of multiple hexagonal areas, each of which is called a cell, that you can clearly make out in the images. The hexagonal grid is efficient, as each cell tower sits at the intersection of three cells, and each of the three directional antennas on top of the tower covers a 120-degree slice of the landscape.”

“To make sure his illustrations were as accurate as possible, Lamm worked with two professors of electrical and computer engineering: Danilo Erricolo at the University of Illinois at Chicago and Fran Harackiewicz at Southern Illinois University in Carbondale.”

What if you had an app on a tablet that let you (roughly) visualize a part of the EM field in this very room?

To be clear, no single device can measure every part of the EM field. One would need different sensors to record each part of it. Even when many parts are recorded, there is no useful way to show all of it at once: you’d be piling multiple images on top of each other, leading to a dense, impossible-to-see mess. But you can use a device to measure any one of these, and then display this data on its own:

The EM field can include:

  • radio waves / WiFi signals

  • microwaves

  • infrared

  • visible light

  • ultraviolet

An app created by Richard Vijgen, called Architecture of Radio, visualizes the overlapping signals that envelop us — from cell towers, WiFi routers, and even satellites flying overhead.  The app, at the moment, is site-specific to an installation in Germany. It uses GPS to get the user’s location then finds nearby cell towers using OpenCellID, and has been custom-programmed to map the WiFi routers and Ethernet cables in the exhibition space. It also uses OpenCellID to predict any satellites that might pass overhead. The app then uses this data to visualize the signals swirling around the exhibition-goers, showing what the project’s website refers to as the “infosphere” that we all live in now.

This app lets you visualize the WiFi signals pulsing around you

Now understand that our entire universe is filled with such fields:

AP Physics Learning Objectives

Essential Knowledge 2.A.1: A vector field gives, as a function of position (and perhaps time), the value of a physical quantity that is described by a vector.

a. Vector fields are represented by field vectors indicating direction and magnitude.
b. When more than one source object with mass or electric charge is present, the field value can be determined by vector addition.
c. Conversely, a known vector field can be used to make inferences about the number, relative size, and location of sources.

Content Connection: This essential knowledge does not produce a specific learning objective but serves as a foundation for other learning objectives in the course.

Essential Knowledge 2.A.2: A scalar field gives, as a function of position (and perhaps time), the value of a physical quantity that is described by a scalar. In Physics 2, this should include electric potential.
a. Scalar fields are represented by field values.
b. When more than one source object with mass or charge is present, the scalar field value can be determined by scalar addition.
c. Conversely, a known scalar field can be used to make inferences about the number, relative size, and location of sources.

Content Connection: This essential knowledge does not produce a specific learning objective but serves as a foundation for other learning objectives in the course.