{"id":4905,"date":"2010-07-30T14:10:43","date_gmt":"2010-07-30T14:10:43","guid":{"rendered":"http:\/\/scienceblogs.com\/principles\/2010\/07\/30\/reader-request-borrowing-energ\/"},"modified":"2010-07-30T14:10:43","modified_gmt":"2010-07-30T14:10:43","slug":"reader-request-borrowing-energ","status":"publish","type":"post","link":"http:\/\/chadorzel.com\/principles\/2010\/07\/30\/reader-request-borrowing-energ\/","title":{"rendered":"Reader Request: Borrowing Energy"},"content":{"rendered":"

Commenter miller asks<\/a>:<\/p>\n

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It’s often said that virtual particles can “borrow” energy, as long as it’s for a short enough time to be compatible with the uncertainty principle. This never made sense to me, because the uncertainty principle says that product of uncertainty in energy and uncertainty in time is greater than h-bar over 2, not less than. Please explain.<\/p>\n<\/blockquote>\n

The relevant equation is in the graphic at the top of this blog, just to the right of the title– the one with ΔEΔt. It’s easy to get turned around with this, due to the slightly unfamiliar business of working with inequalities.<\/p>\n

The right way to think about this is to imagine moving the ΔE to the right side of the equation, giving it the form:<\/p>\n

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Δt ≥ h\/2ΔE<\/p>\n<\/blockquote>\n

What this is telling you is that if you want to detect the presence or absence of a particle whose rest mass energy (E = mc2<\/sup>) is equal to ΔE, you need to look for at least<\/em> a time Δt. You can look for longer if you like, but the minimum observation time needed to ensure that the uncertainty in your measurement is less than the energy of the particle. If you look for less time, your energy uncertainty will be bigger than the mass energy, and you can’t be sure whether the particle was really there or not. (Or, more precisely, you can’t be sure it wasn’t a zero mass, zero energy particle, which is close enough to not existing for blog purposes.)<\/p>\n

I talk about this in the Bunnies Made of Cheese<\/a> chapter of How to Teach Physics to Your Dog<\/cite><\/a>, and because I should really take a break from typing on the computer to let my neck loosen up a bit, I will shamelessly quote myself:<\/p\n\n<\/p>\n

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How does this get us bunnies made of cheese? Well, let’s think about applying this uncertainty principle to empty space. If we look at some small region over a long period of time, we can be quite confident that it is empty. Over a short interval, though, we can’t say for certain that it isn’t<\/em> empty. The space might contain some particles, and in quantum mechanics, that means it will.<\/p>\n

Uncertainty about the emptiness of space isn’t as strange as it may seem at first. If a physicist or a stage magician gives a dog a box to inspect at leisure, she can conclusively state that the box is empty. She can sniff in all the corners, check for false bottoms, and make absolutely sure that there’s nothing hiding in some little recess. If she’s allowed only a brief peek or a quick sniff inside the box, though, she can’t be as confident that the box is empty. There might be something tucked into a corner that she wasn’t able to detect in that short time.<\/p>\n

The amount of time needed to determine whether the box is empty also depends on the size of the thing you might expect to find. You don’t need to look for very long to determine whether the box contains Professor Schr\u00c3\u00b6dinger’s famous cat, but if you’re attempting to rule out the presence of a much smaller object–a crumb of a dog treat, say–a more thorough inspection is required, and that takes time . <\/p>\n

The same idea applies to empty space in quantum physics, via the energy-time uncertainty relationship. When we look at an empty box over a long period of time, we can measure its energy content with a small uncertainty, and know that there is only zero-point energy–no particles are in the box. If we only look over a short interval, however, the uncertainty in the energy can be quite large. Since energy is equivalent to mass through Einstein’s famous E = mc2<\/sup>, this means that we can’t be certain that the box doesn’t<\/em> contain any particles. And as with Schr\u00c3\u00b6dinger’s cat, if we don’t know the exact state of what’s in the box, it’s in a superposition of all the allowed states. The cat is both alive and dead, and the box is both empty, and full of all manner of particles, at the same time<\/em>.<\/p>\n<\/blockquote>\n

That’s the basic idea. So, a virtual particle can “borrow” some energy provided it doesn’t stick around long enough for any canine physicists to measure its energy with enough precision to say that it’s there. The energy-time uncertainty principle gives you the minimum time needed to make that measurement, which is the maximum<\/em> time that a particle can get away with “borrowing” energy from the vacuum before it has to disappear again.<\/p>\n

I hope that makes sense. Or at least as much sense as possible under the circumstances.<\/p>\n","protected":false},"excerpt":{"rendered":"

Commenter miller asks: It’s often said that virtual particles can “borrow” energy, as long as it’s for a short enough time to be compatible with the uncertainty principle. This never made sense to me, because the uncertainty principle says that product of uncertainty in energy and uncertainty in time is greater than h-bar over 2,… Continue reading Reader Request: Borrowing Energy<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"1","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13,142,7,23,11],"tags":[],"class_list":["post-4905","post","type-post","status-publish","format-standard","hentry","category-education","category-how-to-teach","category-physics","category-quantum_optics","category-science","entry"],"_links":{"self":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/4905","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/comments?post=4905"}],"version-history":[{"count":0,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/4905\/revisions"}],"wp:attachment":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/media?parent=4905"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/categories?post=4905"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/tags?post=4905"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}